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Factoring x^4 + x^3 + 2x - 4 = 0 (cubic equ)

  1. Dec 7, 2009 #1
    1. The problem statement, all variables and given/known data
    x^4 + x^3 + 2x - 4 = 0


    2. Relevant equations
    N/A


    3. The attempt at a solution
    x^4 + x^3 + 2x - 4 = 0
    x(x^3 + x^2 +2) = 4

    i don't know what to do with this. i tried to factor (x^3 + x^2 +2), but i don't know how. I also have a feeling that I am not doing this correctly and that there should be a zero instead of a 4 on the right hand side of the equal sign...
     
  2. jcsd
  3. Dec 7, 2009 #2

    Borek

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  4. Dec 7, 2009 #3

    Matterwave

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    I don't think there is, in general, a good way to factor a 4th degree polynomial. You can try synthetic division, if you think you have one factor: (x-1).
     
  5. Dec 7, 2009 #4

    Borek

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    1 and -2 are between obvious root candidates pointed to by the rational root theorem - so you have just used it.

    Besides, you have also just solved the question for the OP, which is exactly a thing that you should not do.
     
  6. Dec 7, 2009 #5
    Oops, my bad. Also, I most definitely did not use rational root theorem; I used guessing. Just because I guess something and there exists a theorem that says my guess is good, doesn't mean I know or in any way care about the theorem. :-) Still, obviously it's a nice thing to know -- I wasn't thinking at all when posting.
     
  7. Dec 7, 2009 #6

    Borek

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    :rofl: happens to everyone :wink:
     
  8. Dec 7, 2009 #7

    HallsofIvy

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    But the polynomial he gets after factoring out x-1 is a cubic. Perhaps that is what he was talking about.

    And the rational root theorem works nicely to find a rational root of that cubic, leaving just a quadratic equation to be solved. (The quadratic has complex roots.)
     
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